Near optimal compression with respect to a static dictionary on a practical massively parallel architecture

We consider sublinear massively parallel algorithms for compressing text with respect to a static dictionary. Algorithms for the PRAM model can do this optimally in O(m+log(n)) time with n processors, where m is the length of the longest entry in the dictionary and n is the length of the input string. We consider what is perhaps the most practical model of massively parallel computation imaginable: a linear array of processors where each processor is connected only to its left and right neighbors. We present an algorithm which in time O(km+mlog(m)) with n/(km) processors is guaranteed to be within a factor of (k+1)/k of optimal, for any integer k⩾1. We also present experiments indicating that performance may be even better in practice